English

Extreme commutative quantum observables are sharp

Quantum Physics 2011-07-12 v2 Mathematical Physics math.MP

Abstract

It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM is an extreme point in the convex set of all POVMs if and only if it is a PVM. This results implies that non-commutativity is a necessary ingredient to overcome the limitations of PVMs.

Keywords

Cite

@article{arxiv.1106.4295,
  title  = {Extreme commutative quantum observables are sharp},
  author = {Teiko Heinosaari and Juha-Pekka Pellonpää},
  journal= {arXiv preprint arXiv:1106.4295},
  year   = {2011}
}

Comments

5 pages, minor corrections in v2

R2 v1 2026-06-21T18:25:41.059Z